The Surface response around a sharply resonant surface polariton mode is simply a Lorentzian

At the planar interface between a material and vacuum, the complex surface response S(omega)=[eps(omega) 1]/[eps(omega)+1], with eps(omega) the relative complex dielectric permittivity of the material, exhibit resonances, typical of the surface polariton modes, when eps(omega) ~ 1. We show that for a moderately sharp resonance, S(omega) is satisfactorily described with a mere (complex) Lorentzian, independently of the details affecting the various bulk resonances describing ) eps(omega). Remarkably, this implies a quantitative correlation between the resonant behaviors of Re[S(omega)] and Im[S(omega)], respectively associated to dispersive and dissipative effects in the surface near-field. We show that this "strong resonance" approximation easily applies, and discuss its limits, based upon published data for sapphire, CaF2 and BaF2. Extension to interfaces between two media or to a non planar interface is briefly considered.